1. Given the points a (2,3), B (5,4) and C (7,10), if the vector AP = AB + λ AC (λ∈ R), what is the value of λ, the point P is in the third quadrant? 2. (1) it is proved that three non parallel vectors a, B and C can form a triangle (the starting point of each vector coincides with the end point of one of the other two vectors) if and only if a + B + C = 0 (2) It is proved that three midline vectors of a triangle can form a triangle (3) In △ ABC, e and F are points on AC and AB, respectively. Be and CF intersect at point g. given CE = 1 / 3CA, BF = 2 / 3ba, calculate the constants λ and μ, such that GE = λ be, GF = μ CF & # 61549;, # 61472 3. As shown in figure 5-3-19, e and F are the edges of ABCD, ad and the midpoint of CD, and be, BF and diagonal AC intersect at points R and t respectively Verification: ar = RT = TC 4. Try to prove: the necessary and sufficient condition for the end points a, B and C of three vectors a, B and C with the origin as the starting point to be on the same straight line is that C = α a + β B (α, β ∈ R, and α + β = 1) Before 6 am on the 21st, don't look down on us

1. Given the points a (2,3), B (5,4) and C (7,10), if the vector AP = AB + λ AC (λ∈ R), what is the value of λ, the point P is in the third quadrant? 2. (1) it is proved that three non parallel vectors a, B and C can form a triangle (the starting point of each vector coincides with the end point of one of the other two vectors) if and only if a + B + C = 0 (2) It is proved that three midline vectors of a triangle can form a triangle (3) In △ ABC, e and F are points on AC and AB, respectively. Be and CF intersect at point g. given CE = 1 / 3CA, BF = 2 / 3ba, calculate the constants λ and μ, such that GE = λ be, GF = μ CF & # 61549;, # 61472 3. As shown in figure 5-3-19, e and F are the edges of ABCD, ad and the midpoint of CD, and be, BF and diagonal AC intersect at points R and t respectively Verification: ar = RT = TC 4. Try to prove: the necessary and sufficient condition for the end points a, B and C of three vectors a, B and C with the origin as the starting point to be on the same straight line is that C = α a + β B (α, β ∈ R, and α + β = 1) Before 6 am on the 21st, don't look down on us

one
Let P (x, y)
According to the meaning of the title, AP = (X-2, Y-3), AB + λ AC = (3 + 5 λ, 1 + 7 λ)
Then X-2 = 3 + 5 λ
y-3=1+7λ
That is, x = 5 + 5 λ